5.2 Medians and Centroids
The centroid of a triangle is a point of concurrency for the three medians of the triangle. In the triangle XYZ below, each of the 3 medians has been constructed, and their intersection, point C, is the centroid for the triangle. Remember that the medians connect the vertex of a triangle to the midpoint of the opposite side.
Modify the shape of the triangle by dragging its vertices with the mouse. Change the measures of the angles, the lengths of the sides, and the location of the centroid. Move the vertices in multiple locations to observe changes when...
a) all angles are acute.
b) one angle is obtuse.
c) one angle is a right angle.
and then answer the questions below.
Where is the centroid when the triangle is acute?
Where is the centroid when the triangle is obtuse?
Where is the centroid when the triangle is a right triangle?
What is the exact value of the ratio XC/XD? What is the exact value of the ratio ZC/ZE? What is the exact value of the ratio YC/YF?
Suppose that XD is 18 inches. What would XC equal?
Suppose that FC is 4 inches. What would YC equal?
The centroid of a triangle is the center of gravity, or balance point for the triangle. What does this mean about it's location?